1. Field of the Invention
The present invention relates to a sampling frequency offset estimation apparatus and method to be applied to an orthogonal frequency division multiplexing (OFDM) system. More particularly, the present invention relates to a sampling frequency offset estimation apparatus and a method estimating a phase shift of each pilot subcarrier of a received signal to estimate a sampling frequency offset.
2. Description of the Related Art
In an orthogonal frequency division multiplexing OFDM method, a data stream input in series is converted into parallel data of a predetermined block unit, parallel symbols are multiplexed into orthogonal carrier frequencies so as to convert a wideband transmission into a narrowband parallel transmission. Such an OFDM method is robust to multi-path fading in a wireless communication environment and enables a high speed data transmission.
A pilot subcarrier is used to track a sampling frequency offset in an OFDM system. In a method of using a pilot subcarrier, pilot symbol data, which is data known to a transmitter and a receiver, is transmitted so that the receiver uses the data to perform synchronization. The pilot subcarrier is divided into two sets. In other words, there are a pilot position in a negative subcarrier and a pilot position in a positive subcarrier. The sampling frequency offset is tracked using information as to a linear relationship between an offset and a phase rotation occurring due to an index of the pilot subcarrier.
FIGS. 1A and 1B are views illustrating an effect of a sampling frequency offset in an OFDM system. FIG. 1A is a view illustrating distortions of a phase and an amplitude at 30 parts per million (ppm) at which an 0.5 initial time offset occurs, and FIG. 1B is a view illustrating distortions of a phase and an amplitude at 30 ppm at which a 0.5 initial time offset and a one-sample symbol time offset occur.
FIGS. 2A and 2B are graphs illustrating an estimation of a sampling frequency offset in a related art OFDM system.
FIG. 2A is a graph illustrating an estimation of a sampling frequency offset using a phase difference between pilot subcarriers. Referring to FIG. 2A, the phase difference between the pilot subcarriers can be computed using Equation 1 as follows:Φm,p−Φm,p+1=−2πΔkΔt/N   [Equation 1]
wherein Φm,p denotes a pth pilot subcarrier in an mth OFDM symbol, Φm,p+1 denotes a phase of a p+1th pilot subcarrier, Δk denotes a distance between pilot subcarriers, Δt denotes a sampling time offset, and N denotes a Fast Fourier Transform Window Size.
Equation 1 can be expressed with respect to a sampling time offset as follows in Equation 2:
                              Δ          ⁢                                          ⁢                      t                          p              ,                              p                +                1                                                    =                  -                                                    Φ                                  m                  ,                  p                                            -                              Φ                                  m                  ,                                      p                    +                    1                                                                                                      -                2                            ⁢              πΔ              ⁢                                                          ⁢                              k                /                N                                                                        [                  Equation          ⁢                                          ⁢          2                ]            
As shown in Equation 2, a sampling time offset can be computed to estimate a phase slope so as to estimate a sampling frequency offset.
FIG. 2B is a graph illustrating an estimation of a sampling frequency offset using an estimation of a variation in a phase difference between pilot subcarriers with time. Referring to FIG. 2B, the variation in the phase difference between the pilot subcarriers can be computed using Equation 3 as follows:
                                          ɛ            ^                                p            ,                          p              +              1                                      =                              1                          2              ⁢              π                                ⁡                      [                                                            tan                                      -                    1                                                  ⁢                                  {                                                            Im                      ⁡                                              (                                                                                                            R                              l                                                        ⁡                                                          (                                                              p                                +                                1                                                            )                                                                                ⁢                                                                                    R                                                              l                                +                                1                                                            *                                                        ⁡                                                          (                                                              p                                +                                1                                                            )                                                                                                      )                                                                                    Re                      ⁡                                              (                                                                                                            R                              l                                                        ⁡                                                          (                                                              p                                +                                1                                                            )                                                                                ⁢                                                                                    R                                                              l                                +                                1                                                                                      ⁡                                                          (                                                              p                                +                                1                                                            )                                                                                                      )                                                                              }                                            -                                                tan                                      -                    1                                                  ⁢                                  {                                                            Im                      ⁡                                              (                                                                                                            R                              l                                                        ⁡                                                          (                              p                              )                                                                                ⁢                                                                                    R                                                              l                                +                                1                                                            *                                                        ⁡                                                          (                              p                              )                                                                                                      )                                                                                    Re                      ⁡                                              (                                                                                                            R                              l                                                        ⁡                                                          (                              p                              )                                                                                ⁢                                                                                    R                                                              l                                +                                1                                                            *                                                        ⁡                                                          (                              p                              )                                                                                                      )                                                                              }                                                      ]                                              [                  Equation          ⁢                                          ⁢          3                ]            
wherein {circumflex over (ε)}p,p+1 denotes a variation in a phase slope computed using a phase difference between pth and p+1th pilots in 1th and 1+1th OFDM symbols, Δk denotes a distance between pilot subcarriers, and Δt denotes a sampling time offset.
Here, the variation in the phase slope may be estimated using a phase difference between pth and p+1th pilots in a symbol delayed by D instead of the 1+1th OFDM symbol and an 1th symbol.
FIG. 3 is a graph illustrating a relationship between a symbol index and a phase estimated by a conventional sampling frequency offset estimation method. Here, S denotes a point of time at which a one sample shifts and at which a distortion occurring due to a sampling frequency offset is required to be compensated for.
Referring to FIG. 3, a phase of a sampling time offset linearly increases with an increase in time in area L. However, a pilot subcarrier having a phase equal to or more −π or π with time after the area L. Thus, the linearity of a phase between pilot subcarriers is not established. Thus, in a case where an average phase shift depending on an index of a pilot subcarrier is used, a wrong sampling frequency offset may be estimated.
S denotes a point of time at which an average phase slope computed by a plurality of pilot subcarriers varies by one sample and at which a sample must be added or deleted due to an effect of noise and thus has a large standard variation. In other words, in a case where an average phase slope of pilot subcarriers is used, a point of time at which a one sample is added or deleted cannot be precisely detected.